Methodology

To identify the key determinants of business cycle synchronisation in the euro area, we employ the extreme-bounds analysis (EBA) as proposed by Leamer and Leonard (1981), Leamer (1983) and further developed by Levine and Renelt (1992), Levine and Zervos (1993), and Sala-i-Martin (1997) in the context of empirical growth analysis. Baxter and Kouparitsas (2004) employ an EBA estimation to explain business cycle synchronisation across a large sample of developing and industrialised countries.

Estimation framework

In empirical studies, the researcher is often faced with the decision which determinants to include in an analysis. Sometimes, various possible regression set-ups have equal theoretical status but the resulting coe¢ cients may depend heavily on the set of control variables employed. Hence, the choice of right-hand side variables is often based on assumptions and, in the end, left to the researcher’s discretion.26 This dilemma, which Brock and Durlauf (2001) refer to as the "open-endedness of theories", may result in incomplete econometric models su¤ering from speci…cation bias.

The EBA framework is one attempt to respond to this dilemma by considering a large number of alternative speci…cations and …ltering out those determinants that do not turn insigni…cant with the alteration of the conditioning set of information. In this sense of

robustness, the signi…cance of the "robust" determinants cannot be eliminated by any other variable. Otherwise, the variable is considered "fragile" even if it is signi…cant in a bivariate or in some multivariate set-ups.

In practice, the robustness of the potential determinants is investigated by testing each candidate variable (M-variable) against a varying set of other conditioning variables (Z-variables). A necessary condition for a variable to be a meaningful determinant of business cycle correlation is that it should be signi…cant in a bivariate regression. Its explanatory power may however vary considerably when other determinants are added to the baseline regression. The basic equation can be expressed as

Y = _iI+ _mM + _zZ+u; (3.1)

where Y denotes a vector of coe¢ cients of bilateral business cycle correlations. The M-variable is the candidate variable of interest which is tested for robustness. This ro- bustness test is conducted by including a varying set of conditioning or control variables, Z, and checking _m’s sensitivity to alterations in Z. For each M-variable, we …rst run a baseline regression without any Z-variables, then successively include one, two, and three Z-variables in every possible combination.27 The I-variable, on the other hand, controls for initial conditions that are exogenous. The "gravity variables", geographical distance and relative population size, fall into that group. We run alternative set-ups with and without the I-variables.

For every M-variable under consideration, the EBA identi…es the "extreme bounds" by constructing the highest and lowest values of con…dence intervals of the estimated _m coe¢ cients. In other words, the extreme upper bound (EUB) is equal to the maximum estimated _m, plus two times its standard error,

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EU B= max_m + 2 ( max_m );

the extreme lower bound (ELB) is the minimum estimated _m, minus two times its standard error,

ELB= min_m 2 ( min_m );

The M-variable is then regarded as robust, if the EUB and the ELB exhibit the same sign and if all estimated _m coe¢ cients are signi…cant.

Leamer’s standard methodology is based on OLS estimates. Estimates of the pa- rameters in cross-section regressions are subject to sampling uncertainty and to cor- relations between sampling errors. Frankel and Rose (1998) and Imbs (2004) use the White correction for heteroskedasticity to account for possible sampling errors. Clark and Van Wincoop (2001) argue that this does not allow to correct for dependencies in the residuals and use GMM methods to calculate the variance-covariance matrix of the parameters. GMM nevertheless gives imprecise variance estimates in small samples and would therefore not have been appropriate in our case, given the relatively small size of our sample consisting in the 66 euro area country pairs. Instead, in order to get robust estimators for the coe¢ cients of the candidate explanatory variables, we apply to the OLS regressions a Newey-West correction for heteroskedasticity and autocorrelation in the residuals which is less dependent on large sample properties.

The decision rule …rst outlined by Levine and Renelt (1992) was derived from the statistical theory expounded in Leamer and Leonard (1981). It has often been criticised for being too restrictive. In practice, an explanatory variable might fail to qualify for robustness because of one statistical outlier in one single equation. Using least absolute deviation (LAD) estimators to deal with potential outliers is, however, not an option for our study because LAD is particularly inappropriate in relatively small samples. Also,

when compared with OLS, LAD is not a robust estimation method in the statistical sense of the word. It indeed requires extra assumptions for the estimation of conditional mean parameters that are not necessarily met in the actual population. Nevertheless, we consider two other criteria in addition to the decision rule de…ned by Levine and Renelt (1992).

The …rst additional criteria is the percentage of signi…cant coe¢ cients of the same sign. Sala-i-Martin (1997) argues that running a su¢ ciently large number of regressions increases the probability of reaching a non-robust result, pointing that "if one …nds a single regression for which the sign of the coe¢ cient _mchanges or becomes insigni…cant, then the variable is not robust."28 _{He suggests to assign a certain "level of con…dence"}

to each M-variable by investigating the share of signi…cant _m coe¢ cients. An M- variable with a share of signi…cant coe¢ cients of 95% may be considered as "signi…cantly correlated" with business cycle synchronisation. In the results tables, we therefore not only state the robust/fragile result but also indicate the share of signi…cant coe¢ cients.29 The second criteria we consider in the cases where one of the bounds changes sign, is whether the value of the extreme bound is large compared with the corresponding coe¢ cients. In some cases, after adding (or subtracting) two standard deviations to the maximum (or minimum) estimated _m coe¢ cient, the extreme upper (or lower) bound changed sign but remained close to around zero while all _m coe¢ cients were signi…cant and of the same sign. When the value of the upper (lower) bound was less than 5% the maximum (minimum) coe¢ cient, we have considered that the variable was signi…cant in explaining business cycle correlation.

These two criteria do not a¤ect our fundamental results but allow to qualify the evidence in one or two limit cases.

2 8_{Sala-i-Martin (1997: 178)} 2 9

We state the share of signi…cant coe¢ cients only for the cases in which at least the bivariate esti- mation coe¢ cient is signi…cant.

Information set

The dependent variable is a vector of bilateral pairs containing the 66 correlation coe¢ - cients between the cyclical part of real GDP for the 12 euro area countries. The candi- date explanatory variables are drawn from the set of potential determinants presented above. They include: bilateral trade, trade openness, trade patterns, economic patterns, bilateral bank ‡ows, real short-term interest rate di¤erentials, nominal exchange rate ‡uctuations, …scal de…cit di¤erentials, national competitiveness indicators, di¤erences in stock market indices, labour market ‡exibility indicators and gravity variables.

Among this set of indicators, we select four main categories ofM-variables of interest

which we think should be key determinants of the business cycle as indicated by the lit- erature. These variables are: bilateral trade and openness to trade, trade specialisation, economic specialisation and bilateral bank ‡ows. Regarding the group of Z-variables, we agree with the selection process used by Levine and Zervos (1993) and try to avoid including series that may overlap with the M-variable under review. This amounts to minimising multicollinearity problems between the explanatory variables which might be a drawback of the EBA analysis. For instance, a similar trade specialisation pattern between two countries may be related to strong intra-industry trade, which would result in an intensi…cation of bilateral trade. The similarity of economic structures may also be re‡ected in the similarity of trade patterns. Strong trade relations may contribute to intensify the ‡ow of credits between two countries. In addition, we test successively for di¤erent alternative measures of these M-variables.

The robustness of the M-variables was tested by estimating multivariate regressions where all possible combinations of 1 to 3 explanatory variables, drawn from a pool of six Z-variables and one I-variable, were added successively to the bivariate regression.

The core group of control Z-variables which may be related to the business cycle includes: bilateral exchange rate volatility (SD_NERE), di¤erences in …scal de…cits (DEFDIFF), di¤erences in national price competitiveness (NCIDIFF), di¤erences in the

performance of stock markets (TOTMKDIFF for the overall market index; alternatively CYSERDIFF for cyclical services), di¤erences in trade union density (TUDDIFF). The employment protection indicator EPADIFF was not used in the multivariate regressions due to the lack of data and absence of signi…cance in the bivariate regression. The Z-variables may also turn out to be potentially important explanatory variables and have also been identi…ed, directly or indirectly, as key determinants of business cycle synchronisation.

To the group of initial Z-variables, we added the gravity variables which we …rst considered asI-variables, and which represent external non-economic factors. However, systematically including geographical distance (GEODIST) in all equations created par- tial correlation problems because several explanatory variables are closely related to ge- ographical distance, bilateral trade in particular. As in Baxter and Kouparitsas (2004), we treated geographical distance as a "not-always" included variable. Including or not di¤erences in population size (POPDIFF) as an I-variable did not make any di¤erence to the EBA analysis. In the tables in appendix B we present the results of the EBA estimates without population di¤erences because of the complete absence of signi…cance of that variable in our estimates.

Robustness tests were conducted also for the variables which we designated ex-ante as Z-variables and I-variables. In order to ensure the comparability of results, the additional explanatory variables were always drawn from the same pool of explanatory variables,30 as for the M-variables.

Samples

In the following sub-sections, for each group of possible explanatory variable, we present the bivariate relations with business cycle and discuss the EBA results. The robustness of the variables is tested for the full sample from 1980 to 2004. It is of particular interest

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to know whether the determinants of business cycle correlation have changed since the implementation of a common monetary policy. We therefore conducted tests for two sub-periods. The …rst period runs from 1980 to 1996, the second period starts in 1997 and ends in 2004. For the above mentioned reasons, we consider the second period as the "EMU period".

Since the analysis is a cross-section analysis, across countries and for one point in time, the sample size for the estimates is always the same whatever the number of years in the period of estimation, and corresponds to the 66 country pairs. Since the series entering the regressions are calculated in terms of averages, the cross-country observations might be more dispersed when calculated over a shorter period of time than when calculated over a period of several years. This is not however the case: the standard deviations of the series scaled by their means are not always higher in the two sub-samples than in the full sample, and in the last sub-sample than the …rst one.

Regarding parameter uncertainty, the standard error of the coe¢ cients tend to in- crease in the 1997-04 sample (see tables of results in appendix B) which could lead to more frequent rejection of robustness. However, there is no automatic link between the size of standard errors and the acceptation or rejection of robustness. The "robustness" of the explanatory variable is accepted also in the cases where the standard error of the explanatory variable’s coe¢ cient increases considerably in the third sample (for instance TRADEPAT in table B.3 or IRSCDIFF in table B.6 in appendix B).